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At
any
moment
these
men
might
have
been
seized
with
horror
at
what
they
were
doing
and
might
have
thrown
up
everything
and
run
away
anywhere
.
But
though
toward
the
end
of
the
battle
the
men
felt
all
the
horror
of
what
they
were
doing
,
though
they
would
have
been
glad
to
leave
off
,
some
incomprehensible
,
mysterious
power
continued
to
control
them
,
and
they
still
brought
up
the
charges
,
loaded
,
aimed
,
and
applied
the
match
,
though
only
one
artilleryman
survived
out
of
every
three
,
and
though
they
stumbled
and
panted
with
fatigue
,
perspiring
and
stained
with
blood
and
powder
.
The
cannon
balls
flew
just
as
swiftly
and
cruelly
from
both
sides
,
crushing
human
bodies
,
and
that
terrible
work
which
was
not
done
by
the
will
of
a
man
but
at
the
will
of
Him
who
governs
men
and
worlds
continued
.
Anyone
looking
at
the
disorganized
rear
of
the
Russian
army
would
have
said
that
,
if
only
the
French
made
one
more
slight
effort
,
it
would
disappear
;
and
anyone
looking
at
the
rear
of
the
French
army
would
have
said
that
the
Russians
need
only
make
one
more
slight
effort
and
the
French
would
be
destroyed
.
But
neither
the
French
nor
the
Russians
made
that
effort
,
and
the
flame
of
battle
burned
slowly
out
.
The
Russians
did
not
make
that
effort
because
they
were
not
attacking
the
French
.
At
the
beginning
of
the
battle
they
stood
blocking
the
way
to
Moscow
and
they
still
did
so
at
the
end
of
the
battle
as
at
the
beginning
.
But
even
had
the
aim
of
the
Russians
been
to
drive
the
French
from
their
positions
,
they
could
not
have
made
this
last
effort
,
for
all
the
Russian
troops
had
been
broken
up
,
there
was
no
part
of
the
Russian
army
that
had
not
suffered
in
the
battle
,
and
though
still
holding
their
positions
they
had
lost
ONE
HALF
of
their
army
.
The
French
,
with
the
memory
of
all
their
former
victories
during
fifteen
years
,
with
the
assurance
of
Napoleon
's
invincibility
,
with
the
consciousness
that
they
had
captured
part
of
the
battlefield
and
had
lost
only
a
quarter
of
their
men
and
still
had
their
Guards
intact
,
twenty
thousand
strong
,
might
easily
have
made
that
effort
.
The
French
who
had
attacked
the
Russian
army
in
order
to
drive
it
from
its
position
ought
to
have
made
that
effort
,
for
as
long
as
the
Russians
continued
to
block
the
road
to
Moscow
as
before
,
the
aim
of
the
French
had
not
been
attained
and
all
their
efforts
and
losses
were
in
vain
.
But
the
French
did
not
make
that
effort
.
Some
historians
say
that
Napoleon
need
only
have
used
his
Old
Guards
,
who
were
intact
,
and
the
battle
would
have
been
won
.
To
speak
of
what
would
have
happened
had
Napoleon
sent
his
Guards
is
like
talking
of
what
would
happen
if
autumn
became
spring
.
It
could
not
be
.
Napoleon
did
not
give
his
Guards
,
not
because
he
did
not
want
to
,
but
because
it
could
not
be
done
.
All
the
generals
,
officers
,
and
soldiers
of
the
French
army
knew
it
could
not
be
done
,
because
the
flagging
spirit
of
the
troops
would
not
permit
it
.
It
was
not
Napoleon
alone
who
had
experienced
that
nightmare
feeling
of
the
mighty
arm
being
stricken
powerless
,
but
all
the
generals
and
soldiers
of
his
army
whether
they
had
taken
part
in
the
battle
or
not
,
after
all
their
experience
of
previous
battles
--
when
after
one
tenth
of
such
efforts
the
enemy
had
fled
--
experienced
a
similar
feeling
of
terror
before
an
enemy
who
,
after
losing
HALF
his
men
,
stood
as
threateningly
at
the
end
as
at
the
beginning
of
the
battle
.
The
moral
force
of
the
attacking
French
army
was
exhausted
.
Not
that
sort
of
victory
which
is
defined
by
the
capture
of
pieces
of
material
fastened
to
sticks
,
called
standards
,
and
of
the
ground
on
which
the
troops
had
stood
and
were
standing
,
but
a
moral
victory
that
convinces
the
enemy
of
the
moral
superiority
of
his
opponent
and
of
his
own
impotence
was
gained
by
the
Russians
at
Borodinó
.
The
French
invaders
,
like
an
infuriated
animal
that
has
in
its
onslaught
received
a
mortal
wound
,
felt
that
they
were
perishing
,
but
could
not
stop
,
any
more
than
the
Russian
army
,
weaker
by
one
half
,
could
help
swerving
.
By
impetus
gained
,
the
French
army
was
still
able
to
roll
forward
to
Moscow
,
but
there
,
without
further
effort
on
the
part
of
the
Russians
,
it
had
to
perish
,
bleeding
from
the
mortal
wound
it
had
received
at
Borodinó
The
direct
consequence
of
the
battle
of
Borodinó
was
Napoleon
's
senseless
flight
from
Moscow
,
his
retreat
along
the
old
Smolénsk
road
,
the
destruction
of
the
invading
army
of
five
hundred
thousand
men
,
and
the
downfall
of
Napoleonic
France
,
on
which
at
Borodinó
for
the
first
time
the
hand
of
an
opponent
of
stronger
spirit
had
been
laid
.
Absolute
continuity
of
motion
is
not
comprehensible
to
the
human
mind
.
Laws
of
motion
of
any
kind
become
comprehensible
to
man
only
when
he
examines
arbitrarily
selected
elements
of
that
motion
;
but
at
the
same
time
,
a
large
proportion
of
human
error
comes
from
the
arbitrary
division
of
continuous
motion
into
discontinuous
elements
.
There
is
a
well-known
,
so-called
sophism
of
the
ancients
consisting
in
this
,
that
Achilles
could
never
catch
up
with
a
tortoise
he
was
following
,
in
spite
of
the
fact
that
he
traveled
ten
times
as
fast
as
the
tortoise
.
By
the
time
Achilles
has
covered
the
distance
that
separated
him
from
the
tortoise
,
the
tortoise
has
covered
one
tenth
of
that
distance
ahead
of
him
:
when
Achilles
has
covered
that
tenth
,
the
tortoise
has
covered
another
one
hundredth
,
and
so
on
forever
.
This
problem
seemed
to
the
ancients
insoluble
.
The
absurd
answer
(
that
Achilles
could
never
overtake
the
tortoise
)
resulted
from
this
:
that
motion
was
arbitrarily
divided
into
discontinuous
elements
,
whereas
the
motion
both
of
Achilles
and
of
the
tortoise
was
continuous
.
By
adopting
smaller
and
smaller
elements
of
motion
we
only
approach
a
solution
of
the
problem
,
but
never
reach
it
.
Only
when
we
have
admitted
the
conception
of
the
infinitely
small
,
and
the
resulting
geometrical
progression
with
a
common
ratio
of
one
tenth
,
and
have
found
the
sum
of
this
progression
to
infinity
,
do
we
reach
a
solution
of
the
problem
.
